Wrinkles In Spacetime

http://fqxi.org/community/articles/display/209

EXCERPT: . . . Hossenfelder is working on identifying experiments that may be able to probe whether spacetime is indeed discrete, allowing physicists to rule out rival theories that have it pinned as continuous. She’s particularly focussing in on potential imperfections in the discreteness. "If spacetime is not fundamentally continuous, then the smoothness we use in general relativity must have defects in it due to quantum effects in its discrete structure," she says. It is a bit like the defects you find within the lattice of a crystal such as a diamond—the underlying structure does not repeat perfectly. And if a particle travelling through spacetime encounters one of these defects then its energy and momentum will be altered. It is these changes that Hossenfelder is hoping to find experimental evidence for....

How a Hypothesis Can Be Neither True Nor False

http://nautil.us/blog/how-a-hypothesis-c...-nor-false

EXCERPT: . . . How is it possible, though, for something to be provably neither provable nor disprovable? An exact answer would take many pages of definitions, lemmas, and proofs. But we can get a feeling for what this peculiar truth condition involves rather more quickly. [...] The Continuum Hypothesis states that there is no infinite collection of real numbers larger than the collection of natural numbers, but smaller than the collection of all real numbers. Cantor was convinced, but could never quite prove [...] It remains possible that new, as yet unknown, axioms will show the Hypothesis to be true or false. For example, an axiom offering a new way to form sets from existing ones might give us the ability to create hitherto unknown sets that disprove the Hypothesis. There are many such axioms, generally known as “large cardinal axioms.” These axioms form an active branch of research in modern set theory, but no hard conclusions have been reached. [...] Put another way: for there to be a proof of the Continuum Hypothesis, it would have to be true in all models of set theory, which it isn’t. Similarly, for the Hypothesis to be disproven, it would have to remain invalid in all models of set theory, which it also isn’t. It remains possible that new, as yet unknown, axioms will show the Hypothesis to be true or false. For example, an axiom offering a new way to form sets from existing ones might give us the ability to create hitherto unknown sets that disprove the Hypothesis. There are many such axioms, generally known as “large cardinal axioms.” These axioms form an active branch of research in modern set theory, but no hard conclusions have been reached....

http://fqxi.org/community/articles/display/209

EXCERPT: . . . Hossenfelder is working on identifying experiments that may be able to probe whether spacetime is indeed discrete, allowing physicists to rule out rival theories that have it pinned as continuous. She’s particularly focussing in on potential imperfections in the discreteness. "If spacetime is not fundamentally continuous, then the smoothness we use in general relativity must have defects in it due to quantum effects in its discrete structure," she says. It is a bit like the defects you find within the lattice of a crystal such as a diamond—the underlying structure does not repeat perfectly. And if a particle travelling through spacetime encounters one of these defects then its energy and momentum will be altered. It is these changes that Hossenfelder is hoping to find experimental evidence for....

How a Hypothesis Can Be Neither True Nor False

http://nautil.us/blog/how-a-hypothesis-c...-nor-false

EXCERPT: . . . How is it possible, though, for something to be provably neither provable nor disprovable? An exact answer would take many pages of definitions, lemmas, and proofs. But we can get a feeling for what this peculiar truth condition involves rather more quickly. [...] The Continuum Hypothesis states that there is no infinite collection of real numbers larger than the collection of natural numbers, but smaller than the collection of all real numbers. Cantor was convinced, but could never quite prove [...] It remains possible that new, as yet unknown, axioms will show the Hypothesis to be true or false. For example, an axiom offering a new way to form sets from existing ones might give us the ability to create hitherto unknown sets that disprove the Hypothesis. There are many such axioms, generally known as “large cardinal axioms.” These axioms form an active branch of research in modern set theory, but no hard conclusions have been reached. [...] Put another way: for there to be a proof of the Continuum Hypothesis, it would have to be true in all models of set theory, which it isn’t. Similarly, for the Hypothesis to be disproven, it would have to remain invalid in all models of set theory, which it also isn’t. It remains possible that new, as yet unknown, axioms will show the Hypothesis to be true or false. For example, an axiom offering a new way to form sets from existing ones might give us the ability to create hitherto unknown sets that disprove the Hypothesis. There are many such axioms, generally known as “large cardinal axioms.” These axioms form an active branch of research in modern set theory, but no hard conclusions have been reached....